A $Γ$-convergence result for 2D type-I superconductors
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912638950178816 |
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| author | Cosenza, Alessandro Goldman, Michael Zilio, Alessandro |
| author_facet | Cosenza, Alessandro Goldman, Michael Zilio, Alessandro |
| contents | We consider a 2D non-standard Modica-Mortola type functional. This functional arises from the Ginzburg-Landau theory of type-I superconductors in the case of an infinitely long sample and in the regime of comparable penetration and coherence lengthes. We prove that the functional $Γ$-converges to the perimeter functional. This result is a first step in understanding how to extend the results of Conti, Goldman, Otto, Serfaty (2018) to the regime of non vanishing Ginzburg-Landau parameter $κ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19587 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A $Γ$-convergence result for 2D type-I superconductors Cosenza, Alessandro Goldman, Michael Zilio, Alessandro Analysis of PDEs 35Q56, 49J10, 49J45, 82D55 We consider a 2D non-standard Modica-Mortola type functional. This functional arises from the Ginzburg-Landau theory of type-I superconductors in the case of an infinitely long sample and in the regime of comparable penetration and coherence lengthes. We prove that the functional $Γ$-converges to the perimeter functional. This result is a first step in understanding how to extend the results of Conti, Goldman, Otto, Serfaty (2018) to the regime of non vanishing Ginzburg-Landau parameter $κ$. |
| title | A $Γ$-convergence result for 2D type-I superconductors |
| topic | Analysis of PDEs 35Q56, 49J10, 49J45, 82D55 |
| url | https://arxiv.org/abs/2504.19587 |